Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an...

The stepped-wedge cluster randomized trial (SW-CRT) design has become popular in healthcare research. It is an appealing alternative to traditional cluster randomized trials (CRTs) since the burden of logistical issues and ethical problems can be reduced. Several approaches for sample size determination for the overall treatment effect in the SW-CRT have been proposed. However, in certain situations we are interested in examining the heterogeneity in treatment effect (HTE) between groups instead. This is equivalent to testing the interaction effect. An important example includes the aim to reduce racial disparities through healthcare delivery interventions, where the focus is the interaction between the intervention and race. Sample size determination and power calculation for detecting an interaction effect between the intervention status variable and a key covariate in the SW-CRT study has not been proposed yet for binary outcomes.

We utilize the generalized estimating equation (GEE) method for detecting the heterogeneity in treatment effect (HTE). The variance of the estimated interaction effect is approximated based on the GEE method for the marginal models. The power is calculated based on the two-sided Wald test. The Kauermann and Carroll (KC) and the Mancl and DeRouen (MD) methods along with GEE (GEE-KC and GEE-MD) are considered as bias-correction methods.

Among three approaches, GEE has the largest simulated power and GEE-MD has the smallest simulated power. Given cluster size of 120, GEE has over 80% statistical power. When we have a balanced binary covariate (50%), simulated power increases compared to an unbalanced binary covariate (30%). With intermediate effect size of HTE, only cluster sizes of 100 and 120 have more than 80% power using GEE for both correlation structures. With large effect size of HTE, when cluster size is at least 60, all three approaches have more than 80% power. When we compare an increase in cluster size and increase in the number of clusters based on simulated power, the latter has a slight gain in power. When the cluster size changes from 20 to 40 with 20 clusters, power increases from 53.1% to 82.1% for GEE; 50.6% to 79.7% for GEE-KC; and 48.1% to 77.1% for GEE-MD. When the number of clusters changes from 20 to 40 with cluster size of 20, power increases from 53.1% to 82.1% for GEE; 50.6% to 81% for GEE-KC; and 48.1% to 79.8% for GEE-MD.

We propose three approaches for cluster size determination given the number of clusters for detecting the interaction effect in SW-CRT. GEE and GEE-KC have reasonable operating characteristics for both intermediate and large effect size of HTE.